Single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state in BCS-BEC crossover

We study the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states for BCS-Bose-Einstein condensation crossover at general temperatures $T$. Because we include the important effects of noncondensed pairs, our $T\ne 0$ phase diagrams are different from those reported in earlier work. We find that generalized LOFF phases may be the ground state for a wide range of (weak through moderately strong) interactions, including the unitary regime. However, these LOFF phases are readily destroyed by nonzero $T$.

Figure 1

(Color online) LOFF1 wave vector $q$ as a function of $1∕k_{F}a$ at $T=0$ and for various $p$. Beyond the turning point, no LOFF1 state exists. The inset shows $T_c$ and mean field $T_c^{\mathrm{MF}}=T^{*}$ (pair formation temperature) at unitarity over respective stability regimes.

Figure 2

(Color online) Phase diagram in the $p$ vs $1∕k_{F}a$ plane for $T∕T_F=0$, 0.05, and 0.1. The dotted region shows where LOFF1 state is unstable but some form of LOFF phase may be stable. The (yellow) light shaded region indicates the stable LOFF1 superfluid and the (cyan) darker shaded region the stable LOFF1 normal state. In contrast to Ref. 16 our calculations do not automatically incorporate phase separation, which is not as universally stable in the presence of a trap.

Figure 3

(Color online) Phase diagram in the $p\text{−}T$ plane for unitary (left), near BCS (middle), and near-BEC (right). The dotted region shows where LOFF1 state is unstable against phase separation but stable generalized LOFF phases may in principle exist. The (yellow) light shaded region is the LOFF1 superfluid, and the (cyan) darker shaded region is the LOFF1 normal state.